few_shots: Example:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Thought: This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.
Answer: G

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000674

5
options: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Understand ratio concepts and use ratio reasoning to solve problems.
problem_activity: Optional activity
The purpose of this activity is for students to find a fractional percent increase.
Look for students who calculate the percentage first and then add them together, and students who multiply by 1.08 and 1.008, respectively.
Launch
Students in groups of 2. 4 minutes of quiet work time followed by partner and then whole-class discussion.
Representation: Internalize Comprehension
. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
The population of City A was approximately 243,000 people, and it increased by 8% in one year. What was the new population?
The population of city B was approximately 7,150,000, and it increased by 0.8% in one year. What was the new population?
Student Response
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Anticipated Misconceptions
Students who want to multiply by
\(1 + \frac{p}{100}\)
may have trouble determining where to put the decimal. Have them think about the problem in steps. How can you find 8%? (Multiply by 0.08.) How can you find 0.8%? (Multiply by 0.008.)
Activity Synthesis
Have selected students show solutions, starting with a solution where the percentage is found first and then added to the initial amount, then the approach where one multiplies by 1.08 or 1.008, respectively. Make sure everyone understands both methods. Help students see the connections between these strategies.
Representing, Speaking: MLR7 Compare and Connect.
Use this routine after students present their solutions for calculating the new population of each city. Ask students, "what is the same and what is different about these approaches?" Call students' attention to the different ways students represented the percent increase in their strategies. These exchanges strengthen students' mathematical language use and reasoning based on percent increases with and without fractional amounts.
Design Principle(s): Maximize meta-awareness


correct_option_index: 0